Comparison of methods for solving the vibrational Schrödinger equation in the course of sequential Monte-Carlo-quantum mechanical treatment of hydroxide ion hydration

Journal
Macedonian Journal of Chemistry and Chemical Engineering
Date Issued
2010-12-15
Author(s)
Petreska, Jasmina
Pejov, Ljupco
Abstract
<jats:p>Three numerical methods were applied to compute the anharmonic O–H stretching vibrational frequencies of the free and aqueous hydroxide ion on the basis of one-dimensional vibrational potential energies computed at various levels of theory: i) simple Hamiltonian matrix diagonalization technique, based on representation of the vibrational potential in Simons-Parr-Finlan (SPF) coordinates, ii) Numerov algorithm and iii) Fourier grid Hamiltonian method (FGH).Considering the Numerov algorithm as a reference method, the diagonalization technique performs remarkably well in a very wide range of frequencies and frequency shifts (up to 300 cm–1). FGH method, on the other hand, though showing a very good performance as well, exhibits more significant (and non-uniform) discrepancies with the Numerov algorithm, even for rather modest frequency shifts.</jats:p>
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J. Petreska, L. Pejov, Comparison of methods for solving the vibrational schrödinger equation in the course of sequential Monte-Carlo-quantum mechanical treatment of hydroxide ionhydration, Macedonian Journal of Chemistry and Chemical Engineering, 29(2), 203–213 (2010).
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